Help with parametric equations

  • Thread starter miglo
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  • #1
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Homework Statement


find parametric equations for the semicircle x^2+y^2=a^2, y>0
using as parameter the slope t=dy/dx of the tangent to the curve at (x,y)


Homework Equations





The Attempt at a Solution


well i know that to parametrize a circle i would use x=acost and y=asint for 0<=t<=2pi
so i guess if i just want the top half i would use 0<=t<=pi ? but im not sure how to use the derivative of y=sqrt(a^2-x^2) to parametrize the curve
i went ahead and found dy/dx to be 1/2(a^2-x^2)^(-1/2)*-2x or -x/sqrt(a^2-x^2)
i dont know what to do next...
 

Answers and Replies

  • #2
Filip Larsen
Gold Member
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Your expression for the slope is correct, but it will probably help you to reduce it a bit more (hint what is a2-x2?).

If we call the slope for s (our parameter), can you then express x as a function of s and y? If so, perhaps you can use this relation to get rid of x in another equation so it ends up only relating y and s, thus allowing you to find y as a function of s. Repeat with y as a function of s and x to get a parameterization for x.
 

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